erweitern (b/a (x-x_{0})+y_{0}-c)^2

Lösung

erweitern

(\frac{b}{a} (x - x_{0}) + y_{0} - c)^{2}

\frac{b ^{2} ( x - x _{0} ) ( x - x _{0} )}{a ^{2}} + \frac{2 b x y _{0} - 2 b x _{0} y _{0} - 2 b c x + 2 b c x _{0}}{a} + y_{0}^{2} - 2 c y_{0} + c^{2}

Schritte zur Lösung

(\frac{b}{a} (x - x_{0}) + y_{0} - c)^{2}

Wende Exponentenregel an:

a^{b + c} = a^{b} \cdot a^{c}

(\frac{b}{a} (x - x_{0}) + y_{0} - c)^{2} = (\frac{b}{a} (x - x_{0}) + y_{0} - c) (\frac{b}{a} (x - x_{0}) + y_{0} - c)

= (\frac{b}{a} (x - x_{0}) + y_{0} - c) (\frac{b}{a} (x - x_{0}) + y_{0} - c)

Setze Klammern

= \frac{b}{a} (x - x_{0}) \frac{b}{a} (x - x_{0}) + \frac{b}{a} (x - x_{0}) y_{0} + \frac{b}{a} (x - x_{0}) (- c) + y_{0} \frac{b}{a} (x - x_{0}) + y_{0} y_{0} + y_{0} (- c) - c \frac{b}{a} (x - x_{0}) - c y_{0} - c (- c)

Vereinfache

\frac{b}{a} (x - x_{0}) \frac{b}{a} (x - x_{0}) + \frac{b}{a} (x - x_{0}) y_{0} + \frac{b}{a} (x - x_{0}) (- c) + y_{0} \frac{b}{a} (x - x_{0}) + y_{0} y_{0} + y_{0} (- c) - c \frac{b}{a} (x - x_{0}) - c y_{0} - c (- c) : \frac{b ^{2} ( x - x _{0} ) ( x - x _{0} )}{a ^{2}} + \frac{2 b x y _{0} - 2 b x _{0} y _{0} - 2 b c x + 2 b c x _{0}}{a} + y_{0}^{2} - 2 c y_{0} + c^{2}

= \frac{b ^{2} ( x - x _{0} ) ( x - x _{0} )}{a ^{2}} + \frac{2 b x y _{0} - 2 b x _{0} y _{0} - 2 b c x + 2 b c x _{0}}{a} + y_{0}^{2} - 2 c y_{0} + c^{2}

e x p an d ((a \cdot x) - b + ((x - (\frac{l}{2})) \cdot c)) \cdot (x - (\frac{l}{2}))

e x p an d (x e^{\frac{1}{x}} - x) \cdot (x \cdot e^{\frac{1}{x}} + x)

e x p an d x (cos (x) - sin (x))

e x p an d (((3 x^{2} + 2 x + 1) \cdot cos (3 x))^{'})^{2021}

e x p an d 16